Problem: Simplify. Rewrite the expression in the form $z^n$. $z^5\cdot z^6=$
Solution: $\begin{aligned} z^5\cdot z^6&=z^{5+6} \\\\ &=z^{11} \end{aligned}$ This follows from the general rule $x^m\cdot x^n=x^{m+n}$. Note that the powers have the same base. We can also see this is correct by expanding the powers. $\begin{aligned} z^5\cdot z^6&=\underbrace{z\cdot z\cdot z\cdot z\cdot z}_\text{5 times}\cdot\underbrace{z\cdot z\cdot z\cdot z\cdot z\cdot z}_\text{6 times} \\\\\\ &=\underbrace{z\cdot z\cdot z\cdot z\cdot z\cdot z\cdot z\cdot z\cdot z\cdot z \cdot z}_\text{11 times} \\\\ &=z^{11} \end{aligned}$ In conclusion, $z^5\cdot z^6=z^{11}$.